Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-18T16:12:36.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Constitutive Laws for Ceramics Exhibiting Stress-Induced Martensitic Transformation

Published online by Cambridge University Press:  25 February 2011

John C. Lambropoulos
John C. Lambropoulos*
Affiliation:
Department of Mechanical Engineering, University of Rochester, Rochester, New York 14627, U.S.A.
Get access

Abstract

The theory of internal variables is used in order to develop multiaxial constitutive laws for ceramics undergoing martensitic stress-assisted transformation, such as partially stabilized zirconia or A12O3-ZrO2. The internal variable is identified with the volume concentration of transformed particles, and we assume that transformation occurs so that the change in potential energy due to the transformation is maximized. When the rate of transformation depends on the applied stresses only through the corresponding change in potential energy, it is shown that the inelastic strain rates are along the normal of a stress function in stress space. The constitutive law depends on all three stress invariants. We further discuss specific stress environments such as crack tip fields, the special case of homogeneous transforming particle distribution, and conditions under which normality is not obeyed.

Type
Articles
Information
MRS Online Proceedings Library (OPL) , Volume 78: Symposium E – Advances in Structural Ceramics , 1986 , 35
Copyright
Copyright © Materials Research Society 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Heuer, A.H., Lange, F.F., Swain, M.V., Evans, A.G., J. Am. Ceram. Soc., 69, 181 (1986).Google Scholar
2. Evans, A.G. and Cannon, R.M., Acta metall., 34, 761 (1986).Google Scholar
3. Becher, P.F., Acta metall., 34, 1885 (1986).CrossRefGoogle Scholar
4. Evans, A.G. and Heuer, A.H., J. Am. Ceram. Soc., 63, 241 (1980).CrossRefGoogle Scholar
5. Meeking, R.M. and Evans, A.G., J. Am. Ceram. Soc., 65, 242 (1982).Google Scholar
6. Olson, G.B. and Cohen, M., in Mechanical Properties and Phase Transformations in Engineering Materials, edited by Antolovich, S.D., Ritchie, R.O. and Gerberich, W.W. (The Metallurgical Society, Warrendale, 1986), p. 367.Google Scholar
7. Leal, R.H., Ph.D. Thesis, M.I.T., 1984.Google Scholar
8. Budiansky, B., Hutchinson, J.W., Lambropoulos, J.C., Int. J. Solids Struct., 19, 337 (1983).Google Scholar
9. Lambropoulos, J.C., Report MECH-55, Harvard Univesity (1984).Google Scholar
10. Chen, I.-W. and Morel, P.E.Reyes, J. Am. Ceram. Soc. 69, 181 (1986).Google Scholar
11. Chen, I.-W. and Chiao, Y.-H., Acta metall., 31, 1627 (1983).CrossRefGoogle Scholar
12. Chen, I.-W. and Chiao, Y.-H., in Advances in Ceramics, vol.12, edited by Claussen, N., Ruhle, M. and Heuer, A.H. (American Ceramic Society, Columbus, 1984), p. 33.Google Scholar
13. Olson, G.B. and Cohen, M., Metall. Trans. A, 13, 1907 (1982).Google Scholar
14. Rice, J.R., in Metallurgical Effects at High Strain Rates, edited by Rohde, R.W. et al. (Plenum, New York, 1973), p. 93.CrossRefGoogle Scholar
15. Rice, J.R., J. Mech. Phys. Solids, 19, 433, 1971.Google Scholar
16. Patel, J.R. and Cohen, M., Acta metall., 1, 531 (1953).Google Scholar
17. Malvern, L.E., Introduction to the Mechanics of a Continuous Medium (Prentice Hall, Englewood Cliffs, 1969), p. 91.Google Scholar
18. Lambropoulos, J.C., J. Am. Ceram. Soc., 69, 218 (1986).Google Scholar